非奇H-矩阵的一个简捷判别定理

设A=(aij)∈Cn×n,若存在α∈(0,1),使i∈N,|aii|≥αRi(A)+(1-α)Si(A),则称A为α-对角占优矩阵。首先推广α-对角占优矩阵的概念到广义α-对角占优矩阵;然后利用α-对角占优矩阵、不可约α-对角占优矩阵、广义严格α-对角占优矩阵等概念及性质,给出了非奇异H-矩阵的一个简捷判别定理。不仅丰富和完善了α-对角占优矩阵与非奇异H-矩阵的理论,更为计算数学、矩阵论、控制论、经济数学等相关领域的研究奠定了基础。

A Simple Criterion for Nonsingular H-Matrix

Let A=(aij)∈Cn×n,if there exists α∈(0,1) which can make |aii|≥αRi(A)+(1-α)Si(A) be right for i∈N,then A is called a α-diagonally dominant matrix.Extend the concept to generalized α-diagonally dominant matrix,and apply the concepts and properties of α-diagonally dominant matrices,irreducible α-diagonally dominant matrices and generalized strictly α-diagonally dominant matrices to obtain a simple criterion of a nonsingular H-matrix.These conclusions not only enrich and improve the theory of α-diagonally dominant matrices and nonsingular H-matrix,but also lay a solid foundation for the research of computational mathematic,matrix theory,control theory,mathematical economics,etc.